Math 152A  Exam #1  REVIEW   April 25, 2011

Instructor Audrey Morrow

Exam covers Chapter 1, Sections  3-8; Chapter 2 Sections 1-5, 8.

My office hour is Mondays & Wednesdays, 1PM – 1:30 in Room A251.  

 

 

A summary of the concepts and topics in Chapter 1:  First, work the "Vocabulary and Readiness Check" in each of the nine sections, to make sure you understand the language.

 

1.  a<b if  __________________     2.  3>1 is the same as 1<3 _______ (T/F)

 

3.  Write the set of integers, using set notation  {…}  ____________________________

 

4.  The absolute value of a real number a is: ____________________________________

 

5.  T/F:  Every whole number is an integer ______ 6.   1/2 is an integer ______  A prime

 

number has divisors __________________  Write 75 as a product of primes._________

 

6.  Be able to add, subtract, multiply and divide using fractions. Be able to find the LCD when needed.  Know the rule for zero in a denominator.  Know how to use exponents, and the Order of Operations.  Simplify  34 and 43       Simplify  (1/2)5       -42  and   (-4)2

 

7.  Know how to evaluate algebraic expressions given replacement values for the variables.   Is 5 a solution to  7x + 8 = -18 + 6x?   Know how to translate phrases such as  "Four times a number, added to 17, is not equal to 26" into their algebraic equivalents.

 

8.  Be able to add, subtract, multiply and divide using signed numbers.  14 + (-27) = ____

 

6(-7) = __________    (-5)(-8) = _____________.  -7/10  +  (-1/10) = ___________

 

What is the opposite of 18? _______  What is the reciprocal of  -7/3?  __________  An

 

opposite may also be called _______________________________.  A reciprocal might

 

also be called ______________________.  9.  During a three-day period, a share of Taco

 

 

 

 

 

 

 

 

 

 

 

 

 

9.  The highest summit in the contiguous United States is Mt Whitney, in California. Its peak stands at an elevation of 14,505  ft.  The lowest point in the contiguous US is also in California, at Badwater Basin in Death Valley.  Badwater Basin’s lowest elevation is 282 ft. below sea level.  What is the difference between those two extremes?

 

 

 

10.  0/3 =  _____________           3/0 = ____________     -5/5 = ________________

 

 

11.  Know the properties of Real Numbers, listed in 1.8.  There are 5 properties plus 2 identities and 2 inverse properties.  Test yourself with Practice problem 6 on page 62.

 

Which properties are shown, and for which operations? 

3(5) = 5(3) shows the commutative property for multiplication.

9(7-3) = 9(7) - 9(3)                 

1(-5) = -5

(-2/5) (-5/2) = 1

(p+5) + 4 = p + (5+4)

N + 0 = N

a + 5 = 5 + a

 

12.  Give an example of the associative property of addition.

 

Chapter 2 topics

 

1.  Be able to identify like terms; know how to combine them:   7xy + 5xy + (-3xy) =

 

 

 

2.  Know how to use the distributive property to remove grouping symbols and simplify expressions like -2(m + 0.3n - 1)             and -(2x -5y + z - 15)

 

 

 

3.  Be able to convert a phrase such as "Subtract 7a-3 from 2a + 8" and to translate words, such as "five added to three times the sum of a number and seven" into algebra.  Practice:  Double a number, minus the sum of the number and six: 

 

 

 

 

 

 

 

 

 

 

4.  Know the two properties of equality, given in class, and on P. 82 in your book.  Know how to use them to solve equations like:  2 = 4(2n-3) - (7n + 4)     and      (4/5) (x) = 16

 

5.  If p is the first of four consecutive odd integers, express their sum in terms of p.

 

 

 

6.  The length of the top of a computer desk is 1.5 feet longer than its width.  If its width measures b feet, express its length in terms of b.

 

 

 

7.  Equivalent equations are equations that have _________________________________

 

8.  Evaluate (-0.8)2                                                       0.82

 

 

9.  Use the Order of Operations to simplify   5  [ -12 -2 (3)2 ]

                                                                               -4 -6 -2

 

10.  Solve the linear equation  y + 2(y+4) = 3(y+3) -7

 

 

 

11.  What does “linear” mean?

 

 

12.  Solve and graph the solution to   -3 < n <  10.  Write your solution in interval notation.

 

 

 

 

13.  Bonus question:  What are the golden and silver rules of equality/inequality?